Maps with dimensionally restricted fibers

Vesko Valov. "Maps with dimensionally restricted fibers." Colloquium Mathematicae 123.2 (2011): 239-248. <http://eudml.org/doc/286652>.

@article{VeskoValov2011,
abstract = {We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber $f^\{-1\}(y)$ belongs to a class S of spaces, then there exists an $F_\{σ\}$-set A ⊂ X such that A ∈ S and $dim f^\{-1\}(y)∖A = 0$ for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all $g ∈ C(X,^\{n+1\})$.},
author = {Vesko Valov},
journal = {Colloquium Mathematicae},
keywords = {Extension dimension; C-spaces; 0-dimensional maps; metric compacta; weakly infinite-dimensional spaces},
language = {eng},
number = {2},
pages = {239-248},
title = {Maps with dimensionally restricted fibers},
url = {http://eudml.org/doc/286652},
volume = {123},
year = {2011},
}

TY - JOUR
AU - Vesko Valov
TI - Maps with dimensionally restricted fibers
JO - Colloquium Mathematicae
PY - 2011
VL - 123
IS - 2
SP - 239
EP - 248
AB - We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber $f^{-1}(y)$ belongs to a class S of spaces, then there exists an $F_{σ}$-set A ⊂ X such that A ∈ S and $dim f^{-1}(y)∖A = 0$ for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all $g ∈ C(X,^{n+1})$.
LA - eng
KW - Extension dimension; C-spaces; 0-dimensional maps; metric compacta; weakly infinite-dimensional spaces
UR - http://eudml.org/doc/286652
ER -